The second day of an appeals hearing for Adrian Peterson concluded in New York this afternoon.

NFL executive Troy Vincent testified today in front of hearing officer Harold Henderson, a former league executive. Vincent, who allegedly told Peterson he would be reinstated with "time served" when his court case cleared, was questioned by NFL Players Association attorney Jeffrey Kessler.

Peterson, the suspended Vikings running back, attended the first part of the hearing on Tuesday but was not in attendance Thursday. He listened from his home in Houston, according to ESPN's Andrew Brandt.

Peterson's NFL-mandated suspension runs until at least April 15.

Henderson, a former NFL Executive Vice President for Labor Relations, was appointed by Commissioner Roger Goodell after the NFLPA requested a third-party arbitrator.

Vincent was unavailable Tuesday because he was testifying on the league's behalf at a Senate committee hearing on domestic violence in professional sports in Washington, D.C.

The focal point of Peterson's appeal is his belief that Vincent told him if he went on the commissioner's exempt list he would get credit for "time served," plus a two-game suspension. A transcript of that conversation, and a recording, were presented at Tuesday's hearing, according to reports.

The NFL has provided no time frame for a ruling, saying that it is up to Henderson. The collective bargaining agreement says that "as soon as practicable following the conclusion of the hearing, the hearing officer will render a written decision which will constitute full, final and complete disposition of the dispute."

Pro Football Talk reported Wednesday that Henderson was urging the sides to negotiate a settlement.

Peterson was deactivated for the team's second game after being indicted by a grand jury in Texas on a felony charge of injury to a child after evidenced surfaced of injuries to a 4-year-old son who had been beaten with a switch.

After a very brief reinstatement protested publicly by some of the league's and team's corporate sponsors, he was placed on the Commissioner's Exempt List while the court case played out. The 2012 NFL MVP plead no contest to a misdemeanor charge of reckless assault on Nov. 4, believing he would be able to rejoin the Vikings.

Peterson has been paid his $11.75 million salary while on the exempt list. His contract, which runs through 2017, had $36 million in guaranteed money that has already been paid out, and his salary next season would be $12.75 million.